# Condensed Matter Seminar: "Formation of a hexagonal limit-periodic structure"

A limit-periodic structure consists of a union of periodic patterns with no largest lattice constant. The discovery of an aperiodic monotile -- a single tile that forces hexagonal limit-periodic pattern in the same way that the two Penrose tiles force a quasicrystalline pattern -- has opened a new path to the theory of formation of a limit-periodic phase and to its possible physical realization. A renormalization analysis shows that the limit-periodic ground state can be reached in a slow quench through an infinite sequence of phase transitions, and numerical studies indicate that the phase is more robust than might be expected from the complexity of the unit tile. Studies of a simple ball-and-spring model with the limit-periodic structure reveal novel extended vibrational modes with arbitrarily low participation ratio.

Physical realization of the model in a colloidal system appears possible, but the fabrication of a suitable particle presents some challenges.